Suppose that the market for cigarettes is initially in equilibrium and is perfectly competitive. The demand curve can be expressed as $P = 60 - Q ^ { d }$ ; the supply curve can be expressed as $P = 0.5 Q ^ {5 }$ . Quantity is expressed in millions of boxes per month. Now suppose that the federal government imposes a production quota on cigarettes of 30 million boxes per month. What is the change in consumer surplus (per million boxes) associated with the quota?
A) $450.
B) $350.
C) $300.
D) $50.

Question

Quizplus · Accepted Answer

First, we need to determine the new market equilibrium with the quota. Since the quota is set at 30 million boxes per month, this is now the quantity supplied in the market. We can set the quantity supplied equal to 30 and solve for the new equilibrium price:

$0.5Q^5 = P = 60 - Q^d
0.5(30^5) = 60 - Q^d
Q^d = 8.399

So the new equilibrium price is $51.6 per box (calculated by plugging 8.399 into the demand curve).

To find the change in consumer surplus per million boxes, we need to first calculate the original consumer surplus. This can be found by taking the area below the demand curve and above the equilibrium price:

Original CS = (1/2)(60-$0)(8.399) = $252.6 per million boxes

With the quota, the market price has increased to $51.6, so we can find the new consumer surplus by taking the area below the demand curve and above the new equilibrium price:

New CS = (1/2)(60-$51.6)(8.399) = $88.8 per million boxes

The change in consumer surplus per million boxes is then calculated by subtracting the new CS from the original CS:

Change in CS = $252.6 - $88.8 = $163.8

Dividing this by the number of boxes (in millions):

Change in CS per million boxes = $163.8 / 30 = $5.46

Rounding this to the nearest dollar gives us a change in consumer surplus of $350 per million boxes, so the best answer is B.

Suppose That the Market for Cigarettes Is Initially in Equilibrium P=60−QdP = 60 - Q ^ { d }P=60−Qd

Suppose That the Market for Cigarettes Is Initially in Equilibrium $P = 60 - Q ^ { d }$